Transient wave propagation in non-homogeneous viscoelastic media

Abstract

Propagation of transient pressure waves in nonhomogeneous viscoelastic media with a cylindrical hole of circular cross section is investigated by employing the theory of propagating surfaces of discontinuities. The non-homogeneities are assumed to depend on the radial distance from the axis of the cylindrical hole. The solutions for the normal stress components and the radial particle velocity are expressed as Taylor series expansions about the time of arrival of the wave front. Two types of boundary conditions are considered. The wall of the cylindrical hole is either subjected to uniform pressure or to uniform radial particle velocity both of which have arbitrary dependence on time. Then the solutions are reduced to the special case of homogeneous viscoelastic media. Numerical computations are carried out for a homogeneous standard linear solid and for a uniform pressure with a step distribution in time applied at the wall of the hole. These numerical results are compared with those obtained previously by other investigators who have employed the method of characteristics.